Anderson Transition, Scaling, and Level Statistics in the Presence of Spin Orbit Coupling

The effect of spin-orbit coupling (SOC) on the localization properties of electrons in two-dimensional disordered systems is investigated by numerical scaling techniques. The Anderson metal-insulator transition in the presence of random SOC is demonstrated by the scaling of the corresponding Lyapunov exponents, and the critical exponents are estimated. At the transition we obtain new universal scale invariant distribution functions for the nearest level spacing distribution function $P\left(S\right)$ and the two point correlation function $K_2\left(\epsilon \right)$ describing the critical spectral density fluctuations.